Temporal characterisation of silicon sensors on Timepix3 ASICs
Elena Dall'Occo, Kazu Akiba, Martin van Beuzekom, Emma Buchanan, Paula Collins, Timothy Evans, Vinicius Franco Lima, Robbert Geertsema, Heinrich Schindler, Hella Snoek, Panagiotis Tsopelas
PPrepared for submission to JINST
Temporal characterisation of silicon sensors on Timepix3ASICs
E. Dall’Occo, 𝑎,𝑑, K. Akiba, 𝑎 M. van Beuzekom, 𝑎 E. Buchanan, 𝑏 P. Collins, 𝑐 T. Evans, 𝑐 V. Franco Lima, 𝑒 R. Geertsema, 𝑎 H. Schindler, 𝑐 H. Snoek, 𝑎 and P. Tsopelas 𝑎, 𝑓 𝑎 Nikhef, Science Park 105, 1098 XG Amsterdam, the Netherlands 𝑏 University of Bristol, Beacon House,Queens Road, BS8 1QU, Bristol, United Kingdom 𝑐 CERN, 1211 Geneve, Switzerland 𝑑 Now at TU Dortmund,Otto-Hahn-Straße 4, 44227 Dortmund, Germany 𝑒 Oliver Lodge Laboratory, University of Liverpool,Liverpool, L69 7ZE, United Kingdom 𝑓 Now at Spectricon, Science and Technology Park of Crete, Heraklion, Greece
E-mail: elena.dall’[email protected]
Abstract: The timing performance of silicon sensors bump-bonded to Timepix3 ASICs isinvestigated, prior to and after different types of irradiation up to 8 × eq cm − . Thesensors have been tested with a beam of charged particles in two different configurations, perpendicularto and almost parallel to the incident beam. The second approach, known as the grazing anglesmethod, is shown to be a powerful method to investigate not only the charge collection, but also thetime-to-threshold properties as a function of the depth at which the charges are liberated.Keywords: Radiation-hard detectors; Hybrid detectors; Solid state detectors; Particle trackingdetectors (Solid-state detectors); Radiation damage to detector materials (solid state); Timingdetectors Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] F e b ontents Understanding the timing capabilities of silicon sensors is fundamental for operation in a high rateenvironment such as the LHC. In view of the upgrade of the LHCb VErtex LOcator (VELO) [1] awide range of prototype sensors have been tested in a beam of charged particles in order to assess theirsuitability. The upgraded VELO is a hybrid silicon pixel detector capable of 40 MHz readout, whichsurrounds the proton-proton collision region and is dedicated to the tracking and reconstruction ofprimary and secondary vertices. The main challenge for the operation of the sensors is the high andnonuniform radiation exposure, with a maximum fluence of 8 × eq cm − , expected atthe closest point to the proton-proton collision after 50 fb − of integrated luminosity. Hence, theprototype sensors have been tested before and after different irradiation types and fluences.– 1 –his paper presents an investigation of the charge collection temporal properties using differentsensor prototypes. The timing performance is determined using a particle beam with two comple-mentary methods: at normal incidence and with a grazing angle [2, 3] approach. The grazing anglemethod consists of analysing particle tracks that traverse the sensor almost parallel to its surface, suchthat the depth that a charge is deposited at can be inferred from the position of the corresponding hitwithin a cluster. The depletion depth of planar sensors can be precisely determined using the grazingangle technique [4]. It has also been applied in charge diffusion studies in silicon [5] and to performintrinsic spatial resolution studies [6]. In this paper, the grazing angle technique has been furtherdeveloped to study the time properties of the sensors as a function of depth. A complementarytechnique for studying sensor properties as a function of depth is the transient current technique(TCT) [7–9], which provides a characterisation and visualisation of the electric field distribution.Two main figures-of-merit are used to quantify the timing performance: the time from when thecharge is liberated to when the signal crosses the threshold on average, referred to as time-to-threshold,and the width of the time-to-threshold distribution, referred to as the temporal resolution.This paper is organised as follows. In Section 2.1 the sensor prototypes are described, followedby the experimental setup in Section 2.2. In Section 2.3 the time-to-threshold measurement methodis discussed. The results for nonirradiated, uniformly neutron irradiated and nonuniformly protonirradiated sensors are presented in Section 3 and Section 4 for sensors placed perpendicularly to thebeam and at grazing angles, respectively. The conclusions are drawn in Section 5. The prototype assemblies tested are hybrid pixel detectors, composed of sensors with 256 × μ m pitch bump-bonded to Timepix3 ASICs [10]. The assemblies are glued to a 635 μ mthick AlN ceramic board and wire-bonded to a custom made kapton-copper hybrid, also glued to theceramic substrate, subsequently read out by a SPIDR system [11].The prototype sensors were produced by two different manufacturers, Hamamatsu Photonics K. K.(HPK) and Micron Semiconductor Ltd . The prototype sensors have different design features,such as pixel implant size, sensor thickness, bulk type, pixel-to-edge (PTE) distance. The maincharacteristics of the assemblies are summarised in Table 1. The details of individual assembliesand their identification numbers, which will be used in the following, can be found in Appendix A. Table 1 . Prototype assemblies.
Vendor Type Thickness PTE Implant widthHPK n-on-p 200 μ m 450, 600 μ m 35, 39 μ mMicron n-on-p 200 μ m 450 μ m 36 μ mMicron n-on-n 150 μ m 250, 450 μ m 36 μ m Hamamatsu Photonics K. K., 325-6, Sunayama-cho, Naka-ku, Hamamatsu City, Shizuoka, 430-8587, Japan Micron Semiconductor Ltd, 1 Royal Buildings, Marlborough Road, Lancing BN158UN, United Kingdom – 2 –he Timepix3 ASIC can simultaneously measure the threshold crossing time, denoted byTime-of-Arrival (ToA), and the time the signal is above threshold, denoted by Time-over-Threshold(ToT). The former is registered with a Time-to-Digital Converter (TDC) with a bin width of 1.56 ns.The latter is related to the energy deposited and is converted into equivalent units of collectedelectrons via a charge calibration process, as described in Ref. [12].Several assemblies were irradiated up to the maximum fluence of 8 × eq cm − ,with some exposed to 24 GeV / 𝑐 protons at IRRAD and others to neutrons at the JSI reactor inLjubljana. The uncertainty on the fluence at both facilities is estimated to be of the order of 10%. Anonuniform irradiation profile is used at IRRAD to emulate the expected conditions of the upgradedVELO. The irradiation profile is reconstructed combining the activation map of the assembly and themeasurement provided by the dosimetry survey. This method is thoroughly described in Ref. [13].The reconstructed fluence profile is shown in Figure 1. An extensive test beam programme has been carried out at the SPS H8 beamline at CERN tocharacterise the sensors. The beam is a mixed charged hadron beam ( ∼
67% protons, ∼
30% pions)at 180 GeV / 𝑐 . The trajectories of particles are reconstructed with the Timepix3 telescope [12], ahigh rate, data-driven beam telescope, composed of two arms of four planes each. Each plane isinstrumented with a 300 μ m p-on-n silicon sensor bump-bonded to a Timepix3 ASIC. The centre ofthe telescope is reserved for the Device Under Test (DUT). The DUT area is equipped with remotelycontrolled motion stages able to translate the DUT in 𝑥 and 𝑦 directions (orthogonal to the beamaxis) and to rotate it about the 𝑦 axis. A vacuum box can also be installed on the central stage tofacilitate testing of irradiated devices at high voltage. The DUT can be cooled down to temperaturesof about − ◦ C.The pointing resolution at the DUT position is about 1 . μ m, enabling intrapixel studies of thesensor. The typical temporal resolution on a track using only timestamps of the telescope Timepix3planes is about 350 ps. In the grazing angle configuration, an excellent temporal resolution is F l u e n ce [ M e V n e q c m − ] R o w Figure 1 . Reconstructed fluence profile. – 3 –seful as clusters can be associated to tracks only using the timing information, which avoids thecomplexities of performing the association with only one spatial dimension.
The time-to-threshold of a hit is obtained by subtracting the track time provided by the telescopefrom the hit time measured in the DUT. There is a constant offset between the track and DUT hittimes due to time-of-flight and differences in cable length between the DUT and the telescope planes,and hence only trends in the time-to-threshold are meaningful. The most probable value of thetime-to-threshold is determined by fitting the distribution with a Cruijff [14] function, a Gaussianfunction with different left-right widths and non-Gaussian tails 𝑓 ( 𝑥 ; 𝑥 , 𝜎 𝐿 , 𝜎 𝑅 , 𝛼 𝐿 , 𝛼 𝑅 ) = exp (cid:0) − ( 𝑥 − 𝑥 ) ( 𝜎 𝐿 + 𝛼 𝐿 ( 𝑥 − 𝑥 ) ) (cid:1) , if 𝑥 < 𝑥 , exp (cid:0) − ( 𝑥 − 𝑥 ) ( 𝜎 𝑅 + 𝛼 𝑅 ( 𝑥 − 𝑥 ) ) (cid:1) , if 𝑥 > 𝑥 , (2.1)where 𝑥 is the mean, 𝜎 𝐿,𝑅 is the left-right width and 𝛼 𝐿,𝑅 parametrises the left-right tail. Anexample of the fit to the time-to-threshold distribution is shown in Figure 2. Unless otherwise stated,the quoted resolution corresponds to the right width of the Cruijff function. The measured resolutionis the sum in quadrature of the intrinsic resolution of the DUT and the resolution of the telescope, of350 ps [12]. The resolution of the DUT can be described by a combination of three terms [15] 𝜎 𝑡 = (cid:18) (cid:20) 𝑡 𝑟 𝑉 th 𝑆 (cid:21) RMS (cid:19) + (cid:18) 𝑡 𝑟 𝑆 / 𝑁 (cid:19) + (cid:18) TDC bin √ (cid:19) , (2.2)where the first component is the contribution from timewalk, the second component is the contributionfrom jitter, and the last component is the contribution from TDC binning. Here 𝑡 𝑟 is the rise time ofthe signal at the output of the amplifier, 𝑉 th is the threshold of the discriminator, 𝑆 is the amplitudeof the signal, 𝑁 is the noise of the front-end, and TDC bin is the TDC bin width. The additionalcontribution from different time offsets within the pixel matrix is consistent between all ASICs [16]and thus is neglected.In order to understand the charge collection time, the effects of the sensor must be disentangledfrom those of the ASIC. It is particularly important to correct for timewalk after irradiation due to thedegraded charge collection. For studies at normal incidence, the timewalk curve is determined perpixel by injecting a test pulse with known charge in the pixel front-end. Conversely, the grazing anglemethod has the advantage that the timewalk curve can be determined directly from the testbeamdata, by selecting only charges liberated at small depth, up to about 25 μ m from the pixel electrodes,in order to reduce the effect of the sensor to a negligible level. The timewalk curve obtained withthis method is found to be compatible with that obtained from test pulse data for a subset of theassemblies, an example of which is shown in Appendix B.The timewalk curve is parameterised as 𝑡 ( 𝑞 ) = 𝐴𝑞 − 𝑞 + 𝐶, (2.3)where 𝑡 is the time-to-threshold, 𝑞 is the charge, 𝑞 the charge corresponding to the onset of the– 4 – × C l u s t e r s × C l u s t e r s Figure 2 . Example of a typical time-to-threshold distribution for a sensor irradiated to full fluence aftertimewalk correction (left), and the same distribution mirrored around the y-axis (right), where the right-handside is indicated in red and the left-hand side in green. asymptote, 𝐴 the slope and 𝐶 the offset. The inverse function is used to correct the measuredtime-to-threshold of each hit. Unless otherwise specified, the results shown are corrected fortimewalk. In this section, the time response of the different sensor designs is studied prior to and afterirradiation, with some prototypes exposed to uniform and others to nonuniform irradiation profiles.The prototypes are placed perpendicular to the incident beam, thus the charge is liberated along thethickness of the sensor allowing for a direct measurement of the resolution per pixel.
Five assemblies have been tested prior to irradiation in order to disentangle sensor effects from thosecaused by radiation damage. For these sensors, the resolution and the time-to-threshold are shownas a function of the operating voltage in Figure 3. The resolution for all the sensor types improveswith increasing voltage and saturates at around 0.8 ns. At the highest voltages, the resolution isdominated by contributions from the ASIC. Therefore the resolution saturates at lower voltage thanthe time-to-threshold. The time-to-threshold of the signal decreases with the operation voltageindicating that the electric field is increasing and the charge carriers do not reach their saturationvelocity until a voltage of around 1000 V. All types of sensors achieve a similar temporal resolutionand time-to-threshold at high voltage, while a small difference arises between the different types atlower voltages. – 5 – Voltage [V]0.60.81.01.21.41.6 σ t [ n s ] S11, HPK , µ m implantS8, HPK , µ m implantS25, Micron n-on-pS30, Micron n-on-nS33, Micron n-on-n
10 10 Voltage [V]-0.50.00.51.01.52.02.53.03.54.0 T t T [ n s ] S11, HPK , µ m implantS8, HPK , µ m implantS25, Micron n-on-pS30, Micron n-on-nS33, Micron n-on-n Figure 3 . Resolution (left) and time-to-threshold (right) as a function of operating voltage for differentnonirradiated sensors. Voltage [V]0.81.01.21.41.61.82.0 σ t [ n s ] S17, HPK , µ m implantS22, HPK , µ m implantS24, Micron n-on-pS27, Micron n-on-nS29, Micron n-on-n Voltage [V]-0.20.00.20.40.60.81.01.21.4 T t T [ n s ] S17, HPK , µ m implantS22, HPK , µ m implantS24, Micron n-on-pS27, Micron n-on-nS29, Micron n-on-n Figure 4 . Resolution (left) and time-to-threshold (right) as a function of operating voltage for sensorsirradiated to full fluence at JSI.
The resolution for irradiated sensors is expected to be worse due to an increased jitter in the signal.After irradiation the amount of charge collected, i.e. the signal amplitude 𝑆 , decreases, degradingthe resolution, as can be seen in Eq. 2.2.The resolution for sensors irradiated to 8 × eq cm − is larger compared to thatbefore irradiation, as can be seen from Figure 4 (left). All the sensors show the same trend, withthe resolution improving as the applied bias increases. The resolution still does not saturate at1000 V, indicating that better performance could potentially be achieved by further increasing thebias voltage. Figure 4 shows that the time-to-threshold trend as a function of voltage is similar– 6 –etween the different types of sensor after irradiation. The time-to-threshold is larger than prior toirradiation, especially at a bias voltage below 400 V. It can be concluded that after irradiation to themaximum fluence, the sensors would need to be operated with a voltage of at least 1000 V in orderto minimise the resolution. Additionally, such a high voltage reduces the effect of timewalk, whichis beneficial for the operations of the detector by reducing the probability that hits are recorded inthe subsequent bunch crossing. The resolution is studied as a function of fluence using a nonuniformly irradiated sensor. Figure 5shows the resolution and time-to-threshold of a HPK sensor for two different operating voltages,500 V and 1000 V, with similar trends observed for intermediate voltages. The resolution degradeswith increasing fluence. While increasing the voltage improves the resolution in all cases, as wasalready noted in Figure 4 (left), the performance achieved prior to irradiation is never attained. Thetime-to-threshold for the two different operating voltages is comparable, as was already observed inFigure 4 (right).The variation of the resolution within a pixel for different fluences is investigated in order tounderstand if the observed degradation is localised. The square pixel symmetry is exploited bycombining the data from four quadrants into one in order to maximise the effective sample size for theintrapixel study. The resolution and the time-to-threshold of a slice of 5 μ m centred at 𝑦 = . μ mof the pixel, where the origin is the lower left corner, is shown in Figure 6. The resolution is uniformover the pixel for all fluence levels at an operating voltage of 1000 V.The lower charge near the border gives rise to a higher correction to the cluster time, thusdecreasing the time-to-threshold. Charge multiplication is observed for this sensor, as reportedin [17]. The Most Probable Value (MPV) of the collected charge is presented in Figure 6 inorder to evaluate interplay of the timewalk and high fluence effects. At the highest fluences,7.0 and 7 . × eq cm − , the signal is larger than the immediate lower fluence bin, eq cm − ]0.911.11.21.31.41.5 σ t [ n s ]
500 V1000 V eq cm − ]-0.500.511.522.533.5 T t T [ n s ]
500 V1000 V
Figure 5 . Resolution (left) and time-to-threshold (right) as a function of fluence for different operatingvoltages for a 200 μ m nonuniformly irradiated HPK n-on-p sensor (S8). – 7 –
20 40Intrapixel position [ µ m]11.11.21.31.41.5 σ t [ n s ] eq cm − ] µ m]678910111213 M P V [ k e − ] eq cm − ] Figure 6 . Resolution (left) and MPV of the cluster charge (right) for a slice of 5 μ m centred at 𝑦 = . μ m ofthe pixel as a function of intrapixel position for different fluences for a 200 μ m nonuniformly irradiated HPKn-on-p sensor (S8) operated at 1000 V. The uncertainties are statistical only. . × eq cm − . Despite a higher signal due to charge multiplication, no improvement isobserved in the resolution nor time-to-threshold. The grazing angle technique is used to study the time-to-threshold as a function of the depth atwhich the charge is deposited in the sensor. The charge collection as a function of depth is alsomeasured, providing complementary information to understand the time dependent properties of thesensors. Firstly, the data selection and grazing angle method are described in Section 4.1, followedby the results for nonirradiated sensors in Section 4.2, and uniformly neutron irradiated sensors andnonuniformly proton irradiated sensors in Sections 4.3 and 4.4, respectively.
In the grazing angle setup, the sensor is placed almost parallel to the beam such that the incidentparticle traverses multiple adjacent pixels, as illustrated in Figure 7. Only clusters on the DUT thatare associated to tracks reconstructed by the telescope are used. A cluster is considered associatedto a track if the time difference between the two is less than 10 ns, where the time of the cluster isdefined as the earliest timestamp amongst its constituent pixel hits. Given the average rate at theCERN SPS of 2M tracks for a spill of 4 . Entry Point
Testbeam meeting – 27/04/2017 A S I C beam s e n s o r θ entry pointexit point ! Entry Point
Testbeam meeting – 27/04/2017 beam δ -ray co l u m n r o w Figure 7 . Illustration of the grazing angle setup. Top view of the sensor (left): the entry and exit point of thetrack are indicated, as well as the angle 𝜃 of the track with respect to the sensor. Front view of the sensor(right): two different types of track are represented, with and without the emission of a 𝛿 -ray. further than three pixels from the edge of the pixel matrix to ensure that the full cluster is within thesensitive volume. The cluster length, which is given by the number of adjacent columns, depends onthe incident angle 𝜃 . The expected cluster length is 𝑁 ( 𝜃 ) = tan 𝜃 × 𝑡 μ m , (4.1)where 𝑁 is the number of pixels forming the cluster and 𝑡 is the active depth of the sensor. Themeasured cluster length for a given angle is distributed around the expected value. A fit to the clusterlength distribution is performed with a Gaussian distribution and clusters with length larger than onestandard deviation from the fitted mean are rejected, removing about 40% of the data.Data sets have been acquired at four angles: 83, 85, 87, 89 degrees. The active depth of thesensor for nonirradiated and uniformly irradiated sensors is determined by performing a fit to theaverage cluster length using Eq. 4.1, where 𝜃 = 𝛼 + 𝜖 with 𝛼 fixed to the chosen angle and 𝜖 allowedto vary to account for a possible offset. The angle offset is found to be of the order of 0 .
05 degrees.As illustrated in Figure 7, the depth 𝑑 ( i ) , defined as the distance from the charge deposit to thepixel implant, can be parameterised by the hit position of the pixel 𝑖 within the cluster by invertingEq. 4.1: 𝑑 ( 𝑖 ) = . μ m × 𝑖 tan 𝜃 . (4.2)Using this relationship, the time needed for the induced signal to cross the threshold (time-to-threshold) is investigated as a function of the depth. A depth of 0 μ m corresponds to the pixelelectrode side, while the full depth, 150 μ m or 200 μ m depending on the sensor, corresponds tothe sensor back side. The following plots are obtained with the sensor placed at a 85 ◦ angle withrespect to the beam, giving a depth step of 55 μ m × cos ( ◦ ) ≈ . μ m, unless otherwise stated. Theuncertainty on the measured depth due to the uncertainty on the angle offset and a possible missinghit at the beginning or end of the cluster is found to have a negligible impact on the charge andtime-to-threshold distributions.The charge collected is measured by performing a fit to the hit charge distribution at a givendepth. Two sources of systematic uncertainty on the MPV are considered, charge calibration anddigitisation. The systematic uncertainty on the charge calibration has two components: due to– 9 –he imperfect knowledge of the injected charge and the statistical uncertainty from the testpulseprocedure. The former is assigned to be 4% of the measured charge, according to Ref. [18]. Thelatter is obtained by generating pseudoexperiments to evaluate how the correlated uncertainties ofthe calibration curve parameters affect the MPV and yields 30 𝑒 − for a nonirradiated sensor and50 𝑒 − for a sensor irradiated at full fluence, where the uncertainty is larger in the irradiated case dueto the smaller charge collected. The digitisation uncertainty is assigned to account for the discretevalues of ToT. This uncertainty is estimated as 40 𝑒 − for hit charges higher than ∼ 𝑒 − , butrapidly increases for lower charges. The effect of this systematic uncertainty on the MPV of thecharge distribution is determined using pseudoexperiments and results in 20 𝑒 − and 50 𝑒 − for anonirradiated sensor and for a sensor irradiated at full fluence, respectively. The results for nonirradiated sensors are shown in Figure 8 for HPK n-on-p (top), Micron n-on-p(middle) and Micron n-on-n (bottom) sensors, in terms of charge collected (left) and time-to-threshold(right) as a function of depth for different bias voltages. It can be seen that the three families ofsensors exhibit the same trend for both the charge collected and time-to-threshold profiles. For anonirradiated sensor and bias voltage above depletion, the MPV of the charge collected is constantand equal to the charge expected for the full thickness of the sensor. The time needed to cross thethreshold is less than 5 ns. The depletion voltage is found to be 120 V and 40 V for HPK and Micronn-on-p, respectively. Below the depletion voltages the charge drops linearly, starting at the borderbetween depleted and nondepleted volume up to a depth of about 20 μ m from the border. This is aneffect due to diffusion known as charge migration [19, 20]. The increase in time-to-threshold withdepth can be mainly attributed to the nonuniformity of the weighting field, which increases towardsthe pixel electrodes, and hence most of the signal is induced while drifting near the electrodes.Since the sensor is nonirradiated and the collected charge is higher than 3000 𝑒 − , the timewalk has anegligible effect. Partially depleted sensors have an additional contribution to the time-to-thresholdfrom charges migrating from the nondepleted region due to diffusion. The trends of the charge collected and time-to-threshold as a function of depth for uniformly irradiatedsensors, as illustrated in Figure 9 for HPK n-on-p, are quite different from the behaviour observedfor nonirradiated devices. Firstly, there is an overall signal reduction due to charge trapping, whichis not fully recovered by an increase in bias voltage. Not all the charge liberated at a given depthis collected and this decreases with distance from the electrodes because charge needs to travelover a longer distance and hence has a larger probability to be trapped. The charge at each biasvoltage shows a slight decrease close to the electrodes. This is due to two different effects: the lowerfield between the neighbouring pixel implants and hole trapping, since for charges liberated close tothe electrodes the current is mainly induced by the motion of holes. Secondly, most of the chargefrom the nondepleted volume recombines before it could be collected. This can be attributed tocharge trapping and slow drift in combination with the integration time of the front-end. The timefor the integration of the signal is limited, hence the discharge can start while still in the process ofintegrating; this is especially relevant for a small amount of charge. A possible effect of a doublypeaked electric field according to the double junction model for highly irradiated sensors [21, 22] is– 10 –
50 100 150 200Depth [ µ m]11.522.533.544.5 M P V [ k e − ]
250 V160 V120 V80 V40 V20 V µ m]-10123456 T t T [ n s ]
250 V160 V120 V80 V40 V20 V µ m]11.522.533.544.5 M P V [ k e − ]
250 V160 V120 V80 V40 V20 V µ m]-10123456 T t T [ n s ]
250 V160 V120 V80 V40 V20 V µ m]11.522.533.544.5 M P V [ k e − ]
100 V40 V20 V15 V µ m]-10123456 T t T [ n s ]
100 V40 V20 V15 V
Figure 8 . Charge collected (left) and time-to-threshold (right) as a function of depth for a 200 μ m thicknonirradiated HPK n-on-p sensor (S6, top), a 200 μ m thick nonirradiated Micron n-on-p sensor (S23, middle)and a 150 μ m thick nonirradiated Micron n-on-n sensor (S34, bottom). A depth of 0 μ m corresponds tothe pixel electrodes side while 200 μ m (top and middle) or 150 μ m (bottom) corresponds to the backside.For the MPVs, the error bars indicate the systematic uncertainties on the measurements, while for thetime-to-threshold, the error bars indicate the statistical uncertainty. – 11 –ot observed. This can be attributed to a combination of the small amount of charge and the lowweighting field at the backside of the sensor.The percentage of charge loss due to irradiation per depth is illustrated in Figure 10 for thedifferent types of sensors and different types of irradiation, where for the sensors nonuniformlyirradiated at IRRAD the region with average fluence of 7 . × eq cm − is selected. Thepercentage of charge lost varies with depth between about 25% close to the electrodes and 60% atthe border of the active region. These values are compatible with what is reported in literature for µ m]11.522.533.544.5 M P V [ k e − ] µ m]-0.500.511.522.53 T t T [ n s ] Figure 9 . Charge collected (left) and time-to-threshold (right) as a function of depth for a 200 μ m thick HPKn-on-p sensor (S22). The dashed line indicates the charge collected by a nonirradiated sensor of the sametype. The sensor is uniformly irradiated to 8 × eq cm − . For the MPVs, the error bars indicatethe systematic uncertainties on the measurements, while for the TtT, the error bars indicate the statisticaluncertainty. µ m]020406080100 C h a r g e L o ss [ % ] S17, HPK, 39 µ m implant, JSIS22, HPK, 35 µ m implant, JSIS8, HPK, 35 µ m implant, IRRADS25, Micron n-on-p, IRRADS29, Micron n-on-n, JSIS30, Micron n-on-n, IRRAD Figure 10 . Percentage of charge loss as a function of depth for a HPK n-on-p and a Micron n-on-p sensorsand for different radiation types. – 12 – µ m]123456 σ t [ n s ] S17, HPK, 39 µ m implant, 1000 VS22, HPK, 35 µ m implant, 1000 VS23, Micron n-on-p 900 VS29, Micron n-on-n 1000 V µ m]-0.500.511.522.533.54 T t T [ n s ] S17, HPK, 39 µ m implant, 1000 VS22, HPK, 35 µ m implant, 1000 VS23, Micron n-on-p 900 VS29, Micron n-on-n 1000 V Figure 11 . Resolution (left) and time-to-threshold (right) as a function of depth for uniformly irradiatedsensors. The circle and square markers indicate the left and right-sided resolution, respectively. similar fluences [23]. The charge loss increases with depth up to the active volume of the sensorafter irradiation, while nothing is collected from the nondepleted volume. A different behaviour isobserved between proton and neutron irradiation, with a steeper dependence on depth in the case ofprotons.The time-to-threshold after timewalk correction increases with depth, up to 2 ns, independent ofthe voltage applied. The different sensors show the same trend in time-to-threshold as a functionof depth, as can be seen in Figure 11 (right). The resolution as a function of depth is shown inFigure 11 (left) and is found to be constant up to around 90 μ m depth. At this point, the right-sidedresolution increases due to residual timewalk. Timewalk corrections are large for these assembliesand therefore the results prior to correction are described in detail in Appendix B. The assemblies presented in this section were irradiated nonuniformly, following the shape of theillumination by the proton beam as shown in Figure 1. All the assemblies have been tested withoutadditional controlled annealing, with the exception of the Micron n-on-n sensor that underwentcontrolled annealing for 80 minutes at 60 ◦ C.The charge collection and time-to-threshold for charges liberated at different depths in the bulkof the sensors are studied as a function of fluence at different operation voltages in Figure 12 andFigure 13 for a HPK n-on-p sensor. The charge is collected only up to ∼ μ m depth from theelectrodes for low voltages, around 250 V, and decreases as a function of fluence. Increasing thebias voltage, the charge is collected from deeper in the sensor, up to ∼ μ m depth at 1000 V. Atthe highest voltage tested, the spread in time-to-threshold with depth is about 1 ns at low fluencesand about 6 ns at 8 × eq cm − , with charge collected more slowly from deeper in thesensor. At a given depth and fluence charge is collected more slowly as the voltage is decreased.Greater precision would be needed to determine any changes in the resolution of the sensor.– 13 – eq cm − ]11.522.533.544.5 M P V [ k e − ] µ m57 µ m86 µ m114 µ m 143 µ m171 µ m200 µ m eq cm − ]11.522.533.544.5 M P V [ k e − ] µ m57 µ m86 µ m114 µ m 143 µ m171 µ m200 µ m eq cm − ]11.522.533.544.5 M P V [ k e − ] µ m57 µ m86 µ m114 µ m 143 µ m171 µ m200 µ m eq cm − ]11.522.533.544.5 M P V [ k e − ] µ m57 µ m86 µ m114 µ m 143 µ m171 µ m200 µ m Figure 12 . Charge collected as a function of fluence from different depths for a 200 μ m HPK n-on-p sensor(S8) operated at 1000 V (top left), at 750 V (top right), at 500 V (bottom left) and at 250 V (bottom right). At depths smaller than 80 µ m, there is a sizeable deviation from the trend for the highest fluenceregion. This effect, observed only at 1000 V bias, is recognised as the so-called charge multiplicationor avalanche effect [24–26]. The charge multiplication happens close to the pixel electrodes wherethe electric field is highest. If charges are liberated in the high field volume, close to the electrodes,they have higher chance to undergo multiplication. In contrast, most of the charges liberated deeperin the bulk will experience trapping before reaching the high field region. A small rise in the apparentMPV is also observed for charges close to the threshold, at a depth that varies as a function of appliedvoltage. This rise can be attributed to a threshold effect, an investigation into which is documentedin Appendix C. Avalanche multiplication is observed in both Hamamatsu n-on-p and Micron n-on-psensors at 1000 V, while the Micron n-on-n sensor does not present any observable effect even atthe highest voltage tested. The charge multiplication effect is not observed for uniformly neutron– 14 – eq cm − ]-202468101214 T t T [ n s ] µ m57 µ m86 µ m114 µ m143 µ m171 µ m200 µ m eq cm − ]-202468101214 T t T [ n s ] µ m57 µ m86 µ m114 µ m143 µ m171 µ m200 µ m eq cm − ]-202468101214 T t T [ n s ] µ m57 µ m86 µ m114 µ m143 µ m171 µ m200 µ m eq cm − ]-202468101214 T t T [ n s ] µ m57 µ m86 µ m114 µ m143 µ m171 µ m200 µ m Figure 13 . Time-to-threshold as a function of fluence from different depths for a 200 μ m HPK n-on-p sensor(S8) operated at 1000 V (top left), at 750 V (top right), at 500 V (bottom left) and at 250 V (bottom right). irradiated sensors, even when operated at 1000 V. This can be attributed to the different nature ofirradiation leading to different damage in the silicon [27].In addition to the absence of the charge multiplication effect, n-on-n sensors present a lowerdegradation as a function of the fluence, as can be seen from Figure 14. The charge collected at adepth of 150 μ m is examined as a function of fluence for different operation voltages in Figure 14(right). It can be seen that the charge collected never falls below the threshold value of 1000 𝑒 − and thus is collected up to the full thickness even at 400V, showing that Micron n-on-n has a largeractive depth compared to the other types of sensors.– 15 – eq cm − ]11.522.533.544.5 M P V [ k e − ] µ m43 µ m64 µ m86 µ m107 µ m129 µ m150 µ m eq cm − ]11.522.533.544.5 M P V [ k e − ] Figure 14 . Charge collected as a function of fluence from different depths for a sensor operated at 1000 V(left) and charge collected as a function of fluence for charges liberated at 150 μ m depths at different operationvoltages (right). The sensor is a 150 μ m Micron n-on-n sensor (S30). The timing properties of a range of prototype sensors are presented in this paper. Several assembliesare studied perpendicular to the incident beam in order to investigate the sensor resolution andtime-to-threshold as a function of bias voltage and fluence. Before irradiation the temporal resolutionsaturates at about 0 .
85 ns slightly before reaching full depletion. After uniform irradiation up to afluence of 8 × eq cm − , the temporal resolution does not saturate up to at least 1000 V.Assemblies irradiated with a non-uniform irradiation profile show that the temporal resolutiondegrades with increasing fluence. It is also observed that with the onset of charge multiplication, thetemporal resolution does not improve.The grazing angle technique proves to be a powerful method to study charge collection andtime-to-threshold properties of charges generated at different depths in the bulk of the sensors. Fornonirradiated sensors the most probable value of collected charge is constant as a function of depthonce full depletion is reached and higher than 3500 𝑒 − . The time-to-threshold is therefore barelyaffected by timewalk. The time-to-threshold is extended by the time needed for the charge to migratefrom the nondepleted volume. For sensors uniformly irradiated to the full fluence it is observed thatmost of the charge collected originates close to the pixel electrode. Due to radiation damage there isa reduction of the charge collected, leading to an increase in timewalk. Otherwise, the temporalcollection properties of the sensor are only marginally affected by radiation damage. Nonuniformlyirradiated sensors allowed the study of charge collection and time-to-threshold variations as afunction of fluence. In particular there is a clear enhancement of charge collected from depths upto 80 μ m at an operating voltage of 1000 V due to charge multiplication for fluences higher than6 × eq cm − . The charge multiplication effect has been observed for proton but notneutron irradiated sensors. – 16 – cknowledgements We would like to express our gratitude to our colleagues in the CERN accelerator departmentsfor the excellent performance of the beam in the SPS North Area. We would like to acknowledgeEugenia Price for her work on the slow controls of the telescope and DUTs, Daniel Saunders for hiscontributions to the online data monitoring and tracking, Mark Williams for his work on the testpulse calibration of the assemblies, and Jan Buytaert, Wiktor Byczynski and Raphael Dumps fortheir extensive and continuous support to keep the telescope operational. We would also like to thankall people that took part in the data taking effort throughout the years of 2014 to 2016. We gratefullyacknowledge the financial support from CERN and from the national agencies: CAPES, CNPq,FAPERJ (Brazil); the Netherlands Organisation for Scientific Research (NWO); The Royal Societyand the Science and Technology Facilities Council (U.K.). This project has received funding fromthe European Union’s Horizon 2020 Research and Innovation programme under Grant Agreementno. 654168. – 17 –
List of assemblies
The details of the assemblies tested are summarised in Table 2.
Table 2 . Assemblies tested.
ID Vendor Thickness[ μ m] Type Edge width[ μ m] Implant[ μ m] Irradiationfacility Peak fluence[10 eq cm − ]S6 HPK 200 n-on-p 450 39 JSI 8S8 HPK 200 n-on-p 450 35 IRRAD 8S11 HPK 200 n-on-p 450 39 IRRAD 8S17 HPK 200 n-on-p 450 39 JSI 8S22 HPK 200 n-on-p 450 35 JSI 8S23 Micron 200 n-on-p 450 36 JSI 8S24 Micron 200 n-on-p 450 36 JSI 8S25 Micron 200 n-on-p 450 36 IRRAD 8S27 Micron 150 n-on-n 450 36 JSI 8S29 Micron 150 n-on-n 450 36 JSI 8S30 Micron 150 n-on-n 450 36 IRRAD 8S33 Micron 150 n-on-n 250 36 - -S34 Micron 150 n-on-n 250 36 - - B Timewalk correction
The timewalk curve obtained from charges liberated up to a depth of about 25 μ m from the electrodesis validated for some assemblies by comparing it to the timewalk curve determined by injecting atestpulse with known charge in the pixel front-end, as shown in Figure 15. The shape variation ofthe timewalk curve is negligible, leading to the conclusion that the profile obtained is sufficientlyrepresentative of a pure electronics effect. The horizontal bar on the hit charge of the testpulse curveis due to the binning and it is not representative of the charge uncertainty.For assemblies irradiated at full fluence, the contribution of timewalk becomes significant, sincethe charge collected is lower than 3000 𝑒 − . The timewalk effect broadens the time-to-thresholddistribution, leading to an asymmetric uncertainty on the single measurement that varies from 3 nsup to 15 ns depending on the depth. In the left plot of Figure 16 the time-to-threshold profile for aHPK n-on-p sensor at 1000 V is compared to the profile obtained by applying the timewalk correctiondescribed in Section 2.3. The timewalk curve is fitted and a correction to the time-to-threshold ofeach hit is applied as a function of charge. The magnitude of the correction increases as the chargedecreases, hence with depth, leading to a smaller mean value and narrower distribution comparedto the uncorrected case. The corrected time-to-threshold spread results in less than 3 ns along thewhole sensor depth and the uncertainty spans from ∼ . ∼ e − ]051015202530 T t T [ n s ] depth < µ mtest pulse Figure 15 . Comparison between timewalk curve from testpulse data and from test beam data with chargesliberated close to the electrode. The sensor is a 200 μ m thick nonuniformly irradiated HPK n-on-p sensor at1000 V bias voltage. µ m]-5051015202530 T t T [ n s ] not correctedcorrected µ m]-4-202468101214 T t T [ n s ] Figure 16 . Comparison between time-to-threshold profiles before and after timewalk correction (left) andcomparison between time-to-threshold profiles for a nonirradiated sensor operated at 250 V and for a uniformlyirradiated sensor operated at 250 V and 1000 V (right). The sensors are 200 μ m thick HPK n-on-p sensors.The uncertainty is assigned as uncertainty on the single measurement. C Rise in MPV close to threshold
A small rise in the measured MPV as a function of fluence is observed in the grazing angle setupclose to the threshold at some depths, as shown in Fig.12. The MPV in some cases should bebelow the threshold from a naive extrapolation from lower fluences, and thus the expected chargedistribution in such cases is investigated using pseudoexperiments. The distribution of charges isgenerated using parameters typical of the real data, and the threshold emulated by selecting only– 19 – e − ]0100200300400500600700 E n tr i e s / . k e − eq cm − ]0.40.60.811.21.41.61.822.22.4 M P V [ k e − ] − . e − / eq cm − − . e − / eq cm − − . e − / eq cm − Figure 17 . Left: Distribution of simulated of charges for an MPV of 800 𝑒 − , demonstrating the effect ofthe threshold on the shape, with the filled histogram indicating the charges that pass the threshold. Right:Comparison with trend observed in a 200 μ m HPK n-on-p sensor operated at 750 V at a depth of 114 μ m,assuming different linear dependence on the true MPV with fluence. charges above 1000 ± 𝑒 − , where the variation is assumed to be gaussian in nature. Both thetrue charge distribution and that with the emulated threshold are shown in Fig. 17 for an MPV of800 𝑒 − . The charge distribution can still be described by a Landau function after the threshold hasbeen applied, albeit with a significantly larger MPV and width. Due to the wide tail of the Landaudistribution, the measured MPV increases as the true MPV decreases, up to a few times the thresholddispersion.This model is compared to the data set where the effect appears most pronounced, at a depth of114 μ m and an applied voltage of 750 V. The true MPV is estimated by assuming a linear decreaseas a function of fluence, with slopes of: − . , − . , − . 𝑒 − / eq cm − considered. TheMPV obtained by performing a fit to the simulated data sets are compared with real data in Fig. 17,where the observed rise in MPV is largest when the true MPV is furthest below threshold. There isqualitatively a good agreement between the data and the model, and thus this effect can account forthe artificial rise in MPV close at very high fluences and close to the threshold.– 20 – eferences [1] LHCb collaboration, LHCb VELO Upgrade Technical Design Report , Tech. Rep.CERN-LHCC-2013-021, CERN, Geneva, 2013.[2] V. Chiochia, M. Swartz, D. Bortoletto, L. Cremaldi, S. Cucciarelli, A. Dorokhov et al.,
Simulation ofthe CMS prototype silicon pixel sensors and comparison with test beam measurements , .[3] S. Meroli, D. Passeri and L. Servoli,
Measurement of charge collection efficiency profiles of CMOSactive pixel sensors , Journal of Instrumentation (2012) P09011.[4] B. Henrich, W. Bertl, K. Gabathuler and R. Horisberger, Depth profile of signal charge collected inheavily irradiated silicon pixels , Tech. Rep. CMS-NOTE-1997-021, CERN, Geneva, Apr, 1997.[5] E. J. Schioppa, J. Idarraga, M. van Beuzekom, J. Visser, E. Koffeman, E. Heijne et al.,
Study of chargediffusion in a silicon detector using an energy sensitive pixel readout chip , IEEE Transactions onNuclear Science (2015) 2349.[6] L. Servoli, S. Meroli, D. Passeri and P. Tucceri, Measurement of submicrometric intrinsic spatialresolution for active pixel sensors , Journal of Instrumentation (2013) P11007.[7] V. Eremin, N. Strokan, E. Verbitskaya and Z. Li, Development of transient current and chargetechniques for the measurement of effective net concentration of ionized charges ( 𝑁 𝑒 𝑓 𝑓 ) in the spacecharge region of p-n junction detectors , Nucl. Instrum. Meth. A (1996) 388.[8] G. Kramberger, V. Cindro, I. Mandic, M. Mikuz, M. Milovanovic, M. Zavrtanik et al.,
Investigation ofIrradiated Silicon Detectors by Edge-TCT , IEEE Trans. Nucl. Sci. (2010) 2294.[9] M. García, J. Sánchez, R. Jaramillo Echeverría, M. Moll, R. Montero, D. Moya et al., On thedetermination of the substrate effective doping concentration of irradiated HV-CMOS sensors using anedge-TCT technique based on the Two-Photon-Absorption process , JINST (2017) C01038.[10] T. Poikela, J. Plosila, T. Westerlund, M. Campbell, M. De Gaspari, X. Llopart et al., Timepix3: A 65kchannel hybrid pixel readout chip with simultaneous ToA/ToT and sparse readout , Journal ofInstrumentation (2014) C05013.[11] J. Visser et al., SPIDR: a read-out system for Medipix3 & Timepix3 , JINST (2015) C12028.[12] K. Akiba et al., LHCb VELO Timepix3 Telescope , .[13] E. Dall’Occo, Search for heavy neutrinos and characterisation of silicon sensors for the VELO upgrade ,Ph.D. thesis, Nikhef, Amsterdam, 2020.[14] BaBar collaboration,
Study of 𝐵 → 𝑋𝛾 decays and determination of | 𝑉 𝑡𝑑 / 𝑉 𝑡𝑠 | , Phys. Rev.
D82 (2010)051101 [ ].[15] N. Cartiglia et al.,
Performance of ultra-fast silicon detectors , Journal of Instrumentation (2014)C02001.[16] K. Heijhoff et al., Timing performance of the LHCb VELO Timepix3 Telescope , Journal ofInstrumentation (2020) P09035.[17] R. Geertsema et al., Charge collection properties of prototype sensors for the LHCb VELO upgrade ,2020.[18] M. Vicente Barreto Pinto,
Caracterização do TimePix3 e de sensores resistentes à radiação paraupgrade do VELO , Ph.D. thesis, Feb, 2016. – 21 –
19] N. Croitoru, P. Rancoita and A. Seidman,
Charge migration contribution to the sensitive layer of asilicon detector , Nuclear Instruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment (1985) 443 .[20] P. Tsopelas,
A silicon pixel detector for LHCb , Ph.D. thesis, 2016.[21] M. Moll,
Displacement damage in silicon detectors for high energy physics , IEEE Trans. Nucl. Sci. (2018) 1561.[22] V. Eremin, E. Verbitskaya and Z. Li, The origin of double peak electric field distribution in heavilyirradiated silicon detectors , Nucl. Instrum. Meth.
A476 (2002) 556.[23] A. Ducourthial et al.,
Performance of thin planar n-on-p silicon pixels after HL-LHC radiation fluences , .[24] M. Mikuz, V. Cindro, G. Kramberger, I. Mandic and M. Zavrtanik, Study of anomalous chargecollection efficiency in heavily irradiated silicon strip detectors , Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (2011) S50 .[25] G. Casse, A. Affolder, P. Allport, H. Brown, I. McLeod and M. Wormald,
Evidence of enhanced signalresponse at high bias voltages in planar silicon detectors irradiated up to . × n 𝑒𝑞 𝑐𝑚 − , NuclearInstruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment (2011) S56 .[26] J. Lange, J. Becker, E. Fretwurst, R. Klanner, G. Kramberger, G. Lindstrom et al.,
Charge multiplicationproperties in highly irradiated epitaxial silicon detectors , PoS
VERTEX2010 (2010) 025.[27] A. Junkes,
Status of defect investigations , Proceedings of Science (2011) .(2011) .